Slides_2010_03_08 - Applied linear algebra and numerical...

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Unformatted text preview: Applied linear algebra and numerical analysis Session 26 Prof. Ulrich Hetmaniuk Department of Applied Mathematics March 8, 2010 Eigenvalue problems Eigenvalue problems give insight into the behavior of evolving systems governed by linear equation. Example: Study of resonance Swing Musical instruments (drum, Helmholtz resonator) Bridges Many other applications... PageRank Algorithm used by Google to rank web pages. The PageRank values are the entries of the dominant eigenvector of the modified adjacency matrix. Review of Linear Dependence Are the following set of vectors linearly dependent? 1 1 , 3 2 1 , 3 1 , Review of Linear Dependence Consider the matrix A = 3 0 0 2 . Are the following set of vectors linearly dependent? x = 1 1 , Ax = 3 2 x = 1 , Ax = 3 x = 1 , Ax = 2 x = x 1 x 2 , Ax = 3 x 1 2 x 2 with x 1 6 = , x 2 6 = = , A0 = Linear Dependence Eigenpairs Consider a non-zero matrix A R n n ....
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Slides_2010_03_08 - Applied linear algebra and numerical...

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